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Question

For a function f(x)0xϵ(a,b);a<bbaf(x)dx=5 then find ba|f(x)|dx ?

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is C 5
We have seen that baf(x)dxba|f(x)|dx But we are given that f(x)0xϵ(a,b)
So, | f(x)| = f(x) . And baf(x)dx will be a positive value as f(x) is always positive in the given interval and also a < b (given). So basically both the modes are redundant.
.ba|f(x)|dx=baf(x)dx
&|baf(x)dx|=baf(x)dx
Thus, ba|f(x)|dx=|baf(x)dx|=5
Note - If there was no information given about f(x) being positive in the interval and also about the limits
(a & b) then the answer could be 5 & 6 both. As |baf(x)dx|ba|f(x)|dx will always hold good.

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